High-performance band-pass modulators of the sigma-delta (ΣΔ) type high-performance are used in many communication systems, such as in audio signal, MPX, and medium frequency (i.e., 10.7 MHz) modulators. Some of the desired requirements of such modulators include high dynamic range, compact size, and low power dissipation.
A band-pass structure of the sigma-delta (ΣΔ) low-order (usually second-order) multi-bit type is often used to meet such requirements. One problem with band-pass modulators of the sigma-delta type is centering the so-called noise notch (i.e., noise mid-frequency) with a given accuracy, such as within 0.2% with respect to a nominal value (e.g., 10.7 MHz). Yet, without such centering the dynamic range of the output signal from the modulator will be significantly diminished.
A prior art sigma-delta modulator structure 1 is illustratively shown in FIG. 1. The modulator 1 includes an oscillator loop 2 connected between an input terminal IN1 and an output terminal OUT1. The oscillation loop 2 includes first and second integrators 3 and 4, a quantizer 5, and stabilizer 6, all of which are connected in series together between the input terminal IN1 and the output terminal OUT1.
In particular, the stabilizer 6 has a first output terminal feedback-connected via a randomizer 8, a delay element 9, and a first integration coefficient generator 10, to a first summing element 11. The summing element 11 is connected between the input terminal IN1 and the first integrator 3. The stabilizer 6 is also connected to the output terminal OUT1 through a second summing element 7, to which a second output terminal of the stabilizer is also connected.
The modulator 1 also includes a second integration coefficient generator 12 connected between the input terminal IN1 and the first summing element 11. A third integration coefficient generator 13 is connected between the input terminal IN1 and the second integrator 4 through a third summing element 14. The modulator 1 further includes a feedback coefficient generator 15 which is connected between an output terminal of the second integrator 4 and the first summing element 11, and an output verify terminal ROUT1 at an output terminal of the quantizer 5.
In particular, the integration coefficient generators 10, 12 and 13 and the feedback coefficient 15 are provided in a relatively simple manner using appropriate capacitance ratios. It should be noted that, in a conventional modulator as shown in FIG. 1, the following are the factors primarily cause the mid-frequency to shift. First, the capacitive matching of the elements in the modulator 1 changes certain coefficients, particularly the gain g thereof.
Further, the non-ideal nature of the integrators 3 and 4, which have finite gain and band·gain product, introduce respective phase errors b1, b2 and gain errors a1, a2 in accordance with the following general relation:
                                                        y              n                        ⁡                          (              z              )                                                          x              n                        ⁡                          (              z              )                                      =                                                            a                n                            *                              z                                  -                  1                                                                    1              -                                                b                  n                                *                                  z                                      -                    1                                                                                .                                    (        1        )            The drop in performance of the modulator 1 is therefore essentially tied to the base block that includes the oscillation loop 2, which, in turn, includes the two integrators 3, 4 and determines the gain coefficient g.
In particular, the oscillation loop 2 generates two complex conjugate-modulo poles, which ideally are positioned 10.7 MHz from each other, as shown schematically in FIG. 2. The coefficient g and gain error an of the integrators alter the pole angle, while the phase error bn of the integrators alters the pole modulo. Thus, the output noise spectrum from the modulator 1 is as shown schematically in FIG. 3, where the shaded area is the undesired offband noise.
Various prior art self-calibration methods are known in which the pulse response of an open-loop filter is utilized to measure the mid-frequency of the modulated signal. To have this parameter satisfactorily calibrated, however, a sequence of sample responses-to-pulse are to be monitored for an extended length of time. It therefore becomes necessary to control the phase integration error, because the pulse response tapers out in relation to this parameter.
For this purpose, such prior art typically use a master/slave system in which a master circuit is controlled to calibrate the modulator 1, with the modulator forming the slave circuit. This technique involves duplicating the modulator hardware, and is beset with problems of matching the master and slave structures. Such method may also compensate the effect of the finite gain introduced by the integrators, as well as increase the area of the capacitors inside the modulator 1 to achieve a match within less than 0.2%.